1. Field of the Invention
The present disclosure relates to the field of bearing cartridges, and in particular, but not necessarily, to heavy duty bearing cartridges that are suitable for gear boxes that are located in wind turbines.
2. Description of Related Art
The first stage of any bearing selection procedure is to calculate the radial and axial load that is to be supported by the bearing. For a shaft carrying one or more gears, the load at the bearings is produced by the forces generated at the contact point of the gear teeth, by the weight of the gears and shaft, and by any external loads applied to the shaft.
The resultant axial and radial forces carried by the bearings are calculated in magnitude and direction by taking moments and by resolving forces so that for a specific transmitted torque, a single value of the radial and axial load can be derived for each bearing.
In examples where two bearings are mounted close together as a bearing pair at one position on the shaft, and a third bearing is mounted to support the other end of the shaft, the load on the bearing pair can be calculated but the load distribution at each bearing of the pair can only be determined by advanced analysis as shaft and housing deflections and bearing radial internal clearance will affect the distribution.
The second stage of the bearing selection is to use the fatigue life rating formulae to determine the required equivalent catalogue load. The simple rating theory formula for roller bearings is of the form:
      L    10    =            (              C        P            )              10      3      Where:                L10 is the lifetime in million cycles that 90% of bearings will survive. In other words, L10 is the lifetime in million cycles for which less than 10% of bearings will show the onset of fatigue damage;        C is the dynamic equivalent radial load rating for the specific bearing, and may be known as a “catalogue value”; and        P is the calculated dynamic equivalent radial load for the bearing.        
In practice, this basic formula is often replaced by a more complicated calculation which allows much better estimations to be made:
      L    n    =            a      n        ·    a    ·                  (                  C          P                )                    10        3            Where:                Ln is the lifetime in million cycles that (100−n) % of bearings will survive. In other words, Ln is the lifetime in million cycles for which less than n % of bearings will show the onset of fatigue damage;        an is a factor to convert the L10 life to a failure rate above or below n %. For example for n=5% then an=0.62, and for n=1% then an=0.21; and        
According to DIN ISO 281 “a” is a life factor which may encompass many other factors and may increase or decrease the bearing life. The value for “a” can include adjustments for bearing materials, temperature and speed and bearing operating conditions, for example lubrication.
The design data and the catalogue values are used in an attempt to ensure that a statistical number of bearings will not fail due to running at excessive loads.
In addition, it is important to ensure that there are no static conditions that will cause bearings to fail, and the worst static conditions should be checked against a catalogue static value C0.
There is also another criterion that should be considered. Bearings can fail due to too little load, and this can cause the rolling elements of the bearing to rotate at incorrect speeds in relation to a shaft, and therefore cause the bearings to skid or smear. Manufacturers give guidance on the minimum values of load that must be maintained to avoid skidding or smearing. Skidding or smearing is especially likely to cause damage in applications where the bearings are running at above 75% of the recommended maximum speed; are large in diameter; and are running in applications where there are rapid shaft accelerations or decelerations. These are conditions that can be found on the high speed shaft of a typical wind turbine gearbox.
In wind turbine applications, it is possible that during periods of running at rated speed, the variation in wind speed can be such that there are times when the transmitted torque can be zero or negative. During such periods, in order to achieve the minimum loading required to avoid skidding and smearing, a force other than forces generated by transmitting power/operating load is required. Sometimes the shaft weight or external forces can ensure that a suitable load is achieved, but where this is not the case some other method should be used. A known bearing manufacturer, SKF, recommend using preload to achieve the minimum load for taper roller bearings.
“End float” occurs when bearings do not exert any force on a shaft, and “zero end float” occurs when bearings are just touching a shaft but not exerting any force on the shaft. Any force that is applied to the shaft is known as preload.
There are two general configurations to mount taper roller bearings. They can be mounted face to face, known as an ‘X’ arrangement and shown in FIG. 1a, or back to back, known as an ‘O’ arrangement as shown in FIG. 1b. In either configuration it is likely to be necessary to set the bearings to a specific preload or end float after assembly.
According to the ‘X’ arrangement shown in FIG. 1a, the shaft 102, inner ring 104 and rollers 106 can heat up more than the outer ring 108 and housing 110. This heating causes the shaft length to increase and the diameter of the shaft 102 that is in contact with the rollers 106 to also increase. Due to the geometry of the rollers 106, the radial increase and the axial increase of the shaft provide an additive effect as both will cause the force exerted by the shaft 102 on the rollers 106 to increase, thereby increasing the preload on the bearing. This arrangement is severely affected by changes in the temperature of the components, but is commonly used because it is relatively easy to design adequate bearing support and is easy to adjust the preload or end float on assembly.
According to the ‘O’ arrangement shown in FIG. 1 b, the shaft 204 is supported by a first bearing arrangement 207 that comprises a first set of tapered roller bearings 208 located between an inner ring 214 and an outer ring 212, and a second bearing arrangement 209 that comprises a second set of tapered roller bearings 216 located between a second outer ring 220 and a second inner ring 222.
It will appreciated that in use, one or more of the shaft 204, inner rings 222, 214, rollers 208, 216, outer rings 212, 220 and housing 202 will be heated up as the parts move relative to each other. As one or more of the above parts heat up, their physical dimensions increase.
In this example, the bearing arrangements 207, 209 are spaced apart so the cone apices of the outer rings 212, 220 coincide at one point on the centreline of the shaft 204. In this case, radial expansion of the shaft 204 will increase the preload on the bearings 207, 209 and the increased radial dimension of the shaft 204 exerts an increased force on the rollers 208, 216. In contrast, axial expansion of the shaft 204 will decrease preload on the bearings 207, 209 because axial expansion of the shaft 204 causes the shaft 204 to encounter a region of the rollers 218 having an increased diameter. That is, as the shaft 204 axially expands, its contact point moves along, and up, the surface of the rollers 208, 216. In the example shown in FIG. 1b it can be difficult to find a method to assemble and adjust the preload or end float.
In order to design such bearing arrangements that do not fail due to thermal expansion, a theoretical analysis is performed as discussed above. The simple form of such analysis assumes that the shaft 204, inner rings 214, 222 and tapered roller bearings 208, 216 (which may be known as the inner components) are made of the same material and are heated by the same amount to a first temperature when in use. In addition, the housing 202 and the outer rings 212, 220 (which may be known as the other components) are also assumed to be made of the same material as each other and also subjected to the same heating to a second temperature. The first temperature is assumed to be greater than the second temperature, and for ease of analysis, the temperature and material of one or more of the components are considered to be uniform.
In the case where all shaft/inner components are at a single temperature and all housing/outer components are at a single, but different, temperature the changes in preload due to radial and axial expansion theoretically cancel out.
In the example shown in FIG. 1b, the angles of the tapered roller bearings 208, 216 are set such that the theoretical roller cone apices intersect on the centreline of the shaft 204. In this way, the axial and radial thermal expansions of the bearing arrangement are theoretically balanced and therefore the preload does not increase when the dimensions of the components of the bearing arrangement 200 increase.
However, in reality there will always be changes in preload as the temperature changes because the temperature of the shaft, inner ring and rollers will not be uniform throughout, and also the temperature of the housing and outer ring will not be uniform. In addition there may be different coefficients of expansion in different components and any interference of rings on the shaft and housing will not behave in the same way as a uniform material.
It can be difficult in practice to mount a shaft in a manner that provides proper axial support for the outer rings and also to satisfactorily set the preload on the bearings for all operating temperatures of the shaft, which does not lead to failure of the bearings.
In addition to the example shown in FIG. 1b, it is possible to have two other conditions of ‘O’ (back-to-back) bearing arrangements, as shown in FIGS. 1c and 1d. For the arrangement shown in FIG. 1c, where the roller cone 302 apices overlap, an increase in shaft 304 temperature causes an increase in preload because the effect of the radial expansion of the shaft 304 outweighs the effect of the axial expansion of the shaft 304.
For the arrangement shown in FIG. 1d, where the roller cone 332 apices do not intersect, an increase in shaft 334 temperature causes a decrease in preload because the effect of the axial expansion of the shaft 334 outweighs the effect of the radial expansion of the shaft 334.
The prior art teaches that back to back and spaced apart arrangements of taper roller bearings are not commonly used because it is hard to engineer a suitable arrangement which allows easy assembly and setting of a desired preload.
FIG. 1e illustrates an alternative prior art bearing arrangement. The bearing arrangement comprises a combination of a cylinder roller bearing 364 and a face-to face taper roller bearing 362. The taper roller bearing 362 takes axial and radial loads, and the cylindrical roller bearing 364 only takes radial loads. It is also possible to use a back to back arrangement for the taper roller bearing pair as shown in FIG. 1f, but in both face to face and back to back arrangements the effect of radial expansion of the shaft 366 makes it impossible to keep the load on the bearings within the desired preload range. It may not be possible to design the taper roller bearing pair in order to meet these design criteria.
The cylinder roller bearing 364 also needs to meet the minimum and maximum loading requirements in the same way as the taper roller bearing pair, and in prior art arrangements this cannot be achieved at zero torque.
Existing calculations reveal that it is not possible to design a bearing arrangement that maintains a preload on the bearings that is sufficient to exceed a 2% minimum load when the shaft is running at zero torque, without the bearings being overloaded at some temperatures within the expected operating range and/or it can be difficult or impossible to set the bearings to the correct preload. The design of the taper roller bearing pair cannot be made to meet these design criteria as discussed in more detail below.
An object of one or more embodiments described herein is to provide an arrangement that can achieve an insignificant change in preload over the full running temperature range of the bearings arrangement and/or shaft, and/or provide a bearing arrangement in a manner that can allow easy and controlled conditions for setting the preload. Also, the bearing cartridge may be easily assembled.
The listing or discussion of a prior-published document or any background in this specification should not necessarily be taken as an acknowledgement that the document or background is part of the state of the art or is common general knowledge. One or more aspects/embodiments of the present disclosure may or may not address one or more of the background issues.